Area enclosed by a circle
From Latin: area  "level ground, an open space,"
The number of square units it takes to exactly fill the interior of a circle.
Try this Drag the orange dots to move and resize the circle. As the size of the circle
changes, the area is recalculated.
A circle is actually a line, one that connects back to itself making a loop. Imagine the circle to be a loop of string.
The string itself has no area, but the space inside the loop does.
So strictly speaking a circle has no area.
However, when we say "the area of a circle" we really mean the area of the space inside the circle.
If you were to cut a circular disk from a sheet of paper, the disk would have an area, and that is what we mean here.
If you know the radius
Given the radius of a circle, the area inside it can be calculated using the formula
where:
R is the radius of the circle
π is Pi, approximately 3.142
See also Derivation of the circle area formula.
If you know the diameter
If you know the diameter of a circle,
the area inside it can be found using the formula
where:
D is the diameter of the circle
π is Pi, approximately 3.142
See also Derivation of the circle area formula.
If you know the circumference
If you know the circumference
of a circle, the area inside it can be found using the formula
where:
C is the circumference of the circle
π is Pi, approximately 3.142
See also Derivation of the circle area formula.
Calculator
Use the calculator on the right to calculate the properties of a circle.
Enter any single value and the other three will be calculated.
For example: enter the radius and press 'Calculate'. The area, diameter and circumference will be calculated.
Similarly, if you enter the area, the radius needed to get that area will be calculated, along with the diameter and circumference.
Try this
 In the figure above, click on "hide details"
 Drag the orange dot on the edge of the circle to make a randomsize circle.
 Now try to estimate the area enclosed by the circle just looking at the squares inside it
When you done click "show details" to see how close you got.
Other circle topics
General
Equations of a circle
Angles in a circle
Arcs
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